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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationFri, 29 Jul 2011 04:29:46 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Jul/29/t13119282959ujt93xdyvt9270.htm/, Retrieved Thu, 16 May 2024 13:06:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123197, Retrieved Thu, 16 May 2024 13:06:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact215

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2011-07-29 08:29:46] [d41d8cd98f00b204e9800998ecf8427e] [Current]
- RMPD    [Kendall tau Correlation Matrix] [] [2011-07-29 21:39:07] [74be16979710d4c4e7c6647856088456]
- RMPD      [(Partial) Autocorrelation Function] [] [2011-07-29 22:27:40] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
494,00
250,00
213,00
113,00
380,00
286,00
533,00
445,00
295,00
150,00
417,00
360,00
700,00
565,00
328,00
112,00
553,00
352,00
434,00
526,00
617,00
333,00
458,00
470,00
385,00
512,00
415,00
397,00
562,00
364,00
576,00
322,00
420,00
560,00
426,00
469,00
571,00
361,00
386,00
363,00
420,00
400,00
575,00
691,00
379,00
408,00
Dataseries Y:
Download CSV
Histogram 
66,67
81,82
85,71
100,00
75,00
80,00
33,33
56,25
75,00
83,33
37,50
72,73
16,67
25,00
60,00
64,52
25,00
50,00
64,29
53,85
75,00
54,55
50,00
57,14
61,54
66,67
64,29
87,50
66,67
75,00
50,00
57,14
61,54
66,67
52,94
87,50
54,55
42,86
90,00
83,33
62,50
66,67
9,00
9,62
31,25
7,55

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123197&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123197&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123197&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean420.56521739130458.6554347826087
Biased Variance17462.202268431498.71242915879
Biased Standard Deviation132.14462633202722.3318702566263
Covariance-1719.41158454106
Correlation-0.56998040726809
Determination0.324877664669497
T-Test-4.60145339259229
p-value (2 sided)3.55180707094357e-05
p-value (1 sided)1.77590353547179e-05
Degrees of Freedom44
Number of Observations46

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 420.565217391304 & 58.6554347826087 \tabularnewline
Biased Variance & 17462.202268431 & 498.71242915879 \tabularnewline
Biased Standard Deviation & 132.144626332027 & 22.3318702566263 \tabularnewline
Covariance & -1719.41158454106 \tabularnewline
Correlation & -0.56998040726809 \tabularnewline
Determination & 0.324877664669497 \tabularnewline
T-Test & -4.60145339259229 \tabularnewline
p-value (2 sided) & 3.55180707094357e-05 \tabularnewline
p-value (1 sided) & 1.77590353547179e-05 \tabularnewline
Degrees of Freedom & 44 \tabularnewline
Number of Observations & 46 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123197&T=1

[TABLE]
[ROW][C]Pearson Product Moment Correlation - Ungrouped Data[/C][/ROW]
[ROW][C]Statistic[/C][C]Variable X[/C][C]Variable Y[/C][/ROW]
[ROW][C]Mean[/C][C]420.565217391304[/C][C]58.6554347826087[/C][/ROW]
[ROW][C]Biased Variance[/C][C]17462.202268431[/C][C]498.71242915879[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]132.144626332027[/C][C]22.3318702566263[/C][/ROW]
[ROW][C]Covariance[/C][C]-1719.41158454106[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.56998040726809[/C][/ROW]
[ROW][C]Determination[/C][C]0.324877664669497[/C][/ROW]
[ROW][C]T-Test[/C][C]-4.60145339259229[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]3.55180707094357e-05[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.77590353547179e-05[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]44[/C][/ROW]
[ROW][C]Number of Observations[/C][C]46[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123197&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123197&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean420.56521739130458.6554347826087
Biased Variance17462.202268431498.71242915879
Biased Standard Deviation132.14462633202722.3318702566263
Covariance-1719.41158454106
Correlation-0.56998040726809
Determination0.324877664669497
T-Test-4.60145339259229
p-value (2 sided)3.55180707094357e-05
p-value (1 sided)1.77590353547179e-05
Degrees of Freedom44
Number of Observations46


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
bitmap(file='test1.png')
histx <- hist(x, plot=FALSE)
histy <- hist(y, plot=FALSE)
maxcounts <- max(c(histx$counts, histx$counts))
xrange <- c(min(x),max(x))
yrange <- c(min(y),max(y))
nf <- layout(matrix(c(2,0,1,3),2,2,byrow=TRUE), c(3,1), c(1,3), TRUE)
par(mar=c(4,4,1,1))
plot(x, y, xlim=xrange, ylim=yrange, xlab=xlab, ylab=ylab)
par(mar=c(0,4,1,1))
barplot(histx$counts, axes=FALSE, ylim=c(0, maxcounts), space=0)
par(mar=c(4,0,1,1))
barplot(histy$counts, axes=FALSE, xlim=c(0, maxcounts), space=0, horiz=TRUE)
dev.off()
lx = length(x)
makebiased = (lx-1)/lx
varx = var(x)*makebiased
vary = var(y)*makebiased
corxy <- cor.test(x,y,method='pearson')
cxy <- as.matrix(corxy$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm','Mean',''),header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased.htm','Biased Variance',''),header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased1.htm','Biased Standard Deviation',''),header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('covariance.htm','Covariance',''),header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('pearson_correlation.htm','Correlation',''),header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('coeff_of_determination.htm','Determination',''),header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('ttest_statistic.htm','T-Test',''),header=TRUE)
a<-table.element(a,as.matrix(corxy$statistic)[1,1],2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value (2 sided)',header=TRUE)
a<-table.element(a,(p2 <- as.matrix(corxy$p.value)[1,1]),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value (1 sided)',header=TRUE)
a<-table.element(a,p2/2,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Degrees of Freedom',header=TRUE)
a<-table.element(a,lx-2,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of Observations',header=TRUE)
a<-table.element(a,lx,2)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')